On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study

Abstract

Ridge regression is a popular method to solve the multicollinearity problem for both linear and non-linear regression models. This paper studied forty different ridge regression t-type tests of the individual coefficients of a linear regression model. A simulation study was conducted to evaluate the performance of the proposed tests with respect to their empirical sizes and powers under different settings. Our simulation results demonstrated that many of the proposed tests have type I error rates close to the 5% nominal level and, among those, all tests except one have considerable gain in powers over the standard ordinary least squares (OLS) t-type test. It was observed from our simulation results that seven tests based on some ridge estimators performed better than the rest in terms of achieving higher power gains while maintaining a 5% nominal size.

Keywords

• empirical power
• multiple linear regression
• mean square error (mse)
• ridge regression
• size of the test
• simulation study
• t-test
• type i error rate